Stability and Hopf bifurcation of a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting

In this paper, a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting subject to the homogeneous Neumann boundary conditions is investigated. Firstly, the global asymptotic stability of the unique positive constant equilibrium is obtained by an iteration technique. Secondly, regarding time delay as a bifurcation parameter and using the normal form theory and center manifold theorem, the existence, stability and direction of bifurcating periodic solutions are demonstrated, respectively. Finally, numerical simulations are conducted to illustrate the theoretical analysis.